The present invention relates to digital communication and storage systems and more particularly to systems and methods for error control.
Error correcting codes insert redundancy into digital information streams so as to reduce susceptibility to noise. Applying an error correcting code at the transmitter permits the receiver to detect and sometimes correct errors induced by noise and/or interference. Some popular types of error correcting codes include convolutional codes, block codes, and Reed Solomon codes, etc.
An important recent development in the topic of error correcting codes is the discovery of xe2x80x9cturboxe2x80x9d codes. These codes typically involve an iterated combination of two or more systematic convolutional codes (codes where the encoder output bits include unaltered input bits.) A key feature of turbo codes is the use of an iterated decoding technique where each successive decoding step outputs soft decisions usable as input to the next decoding step. By employing turbo codes, one may approach the limit of channel capacity in the presence of noise set by the Shannon theorem.
Further work has been done to exploit similar iterated combinations as applied to systematic block codes. See Hagenauer, Iterative Decoding of Binary Block and Convolutional Codes, IEEE Transactions on Information Theory, Vol. 42, No. 2 (March 1996), the contents of which are herein incorporated by reference. What is needed are decoding techniques that allow even closer approach to the limit without undue increase in complexity. It is furthermore desirable to implement the decoder with inexpensive components to the extent possible.
In one embodiment, the present invention augments the performance of iterative soft decision-in soft decision-out decoding of block codes with the use of information based on multiple parity equations inherent to the block codes. Another aspect of the present invention employs cyclic shifting of codewords in the context of iterative soft decision-in soft decision-out decoding to maximize the usefulness of a parity equation corresponding to any particular codeword bit. Yet another aspect of the present invention determines soft decisions on a bit-by-bit basis in response to multi-bit symbol measurements. This provides more coding gain than symbol-by-symbol soft decisions.
According to a first aspect of the present invention, a signal processing system includes a receiver system that receives a series of codewords that have been coded according to an iterative block coding procedure, and a decoder that decodes the series of codewords according to an iterative decoding procedure. At least one iteration of the decoding procedure forms estimates of codeword bits based in part on at least two parity equations inherent to a block code employed in the iteratively applied block coding procedure.
According to a second aspect of the present invention, a method for estimating bit-by-bit soft decision value in a digital communication system where multibit symbols are communicated is provided. The method includes receiving a multibit symbol, for a particular bit of the multibit symbol, evaluating a first Euclidean distance between the multibit symbol and a closest ideal symbol for which the particular bit has value xe2x80x9c1xe2x80x9d, evaluating a second Euclidean distance between the multibit symbol and a closest ideal symbol for which the particular bit has value xe2x80x9c0xe2x80x9d, determining a soft decision value for the particular bit based on the first Euclidean distance and the second Euclidean distance, and using the soft decision value as a basis for an iterative decoding process.